A069830 Multiplicative inverse of prime(n) modulo prime(n+1).

2, 2, 3, 8, 6, 4, 9, 17, 24, 15, 6, 10, 21, 35, 44, 49, 30, 11, 53, 36, 13, 62, 74, 12, 25, 51, 80, 54, 28, 9, 98, 114, 69, 134, 75, 26, 27, 125, 144, 149, 90, 19, 96, 49, 99, 123, 130, 170, 114, 58, 199, 120, 25, 214, 219, 224, 135, 46, 70, 141, 205, 285, 233, 156, 79

Offset

1,1

Comments

Smallest k such that prime(n+1) divides k*prime(n) - 1, n>1.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) + A077005(n) = prime(n+1). - Emmanuel Vantieghem, Aug 12 2018

Example

a(4) = 8 as prime(5) = 11 divides 8*7 -1, where 7 = prime(4).
a(9) = 24, for a(9)*prime(9) = 24*23 = (-5)*(-6) [mod 29] = 1 [mod prime(10)].
a(14) = 35, for a(14)*prime(14) = 35*43 = (-12)*(-4) [mod 47] = 1 [mod prime(15)].

Maple

seq( (1/ithprime(n) mod ithprime(n+1)), n = 1..65); # G. C. Greubel, Aug 09 2019

Mathematica

Table[PowerMod[Prime[n], -1, Prime[n+1]], {n, 65}] (* G. C. Greubel, Aug 09 2019 *)

Prog

(PARI) vector(65, n, lift(Mod(prime(n), prime(n+1))^-1)) \\ Joerg Arndt, Aug 09 2019
(Magma) [InverseMod(NthPrime(n), NthPrime(n+1)): n in [1..65]]; // G. C. Greubel, Aug 09 2019
(Sage) [nth_prime(n).inverse_mod(nth_prime(n+1)) for n in (1..65)] # G. C. Greubel, Aug 09 2019

Crossrefs

Cf. A077005.

Sequence in context: A205374 A056762 A213329 * A153935 A153944 A046652

Adjacent sequences: A069827 A069828 A069829 * A069831 A069832 A069833

Keyword

nonn

Author

Lekraj Beedassy, Apr 23 2002

Extensions

More terms from Rick L. Shepherd, May 03 2002

Status

approved